A Lagrange matrices approach to confluent Cauchy matrices

作者：Verde Star L^*

来源：Linear Algebra and Its Applications, 2004, 389: 249-268.

DOI：10.1016/j.laa.2004.03.018

• Cauchy matrices
• matrix factorization
• matrix inversion
• Lagrange matrices

We present a new approach to study inversion and factorization properties of confluent Cauchy matrices. We consider a class of generalized Vandermonde matrices, called Lagrange matrices, that are connected in a simple way with the Cauchy matrices. We apply the methods introduced in [Adv. Appl. Math. 10 (1989) 348] to obtain inversion and factorization theorems for Lagrange matrices and their confluent forms, and then derive corresponding results for Cauchy matrices. A Lagrange matrix V is associated with a pair of vectors (x(0), x(1),...,x(n)) and (y(0), y(1),...., y(n)). V is the matrix representation of the substitution operator that sends the vector (p(x(0)), p(x(1)),...,p(x(n)))(T) to the vector (p(y(0)), p(y(1)),...,P(y(n)))(T), for any polynomial p of degree at most n.

• 出版日期2004-9-15